# Surface area of a cylinder

*When working out the surface area of a cylinder, remember to consider both circular ends and the curved surface.*

What is the surface area of a cylinder?

The total of both the circular end areas and the curved surface area.

Surface area of cylinder formula

**Cylinder surface area = both circular end areas + curved surface area**

The area of each end of the cylinder is πr² (where π= pi and r = radius of circle) (see also area of a circle). So the area of both ends of the cylinder is 2πr².

The curved surface area is the circumference of the cylinder (2πr - see also circumference of a circle) multiplied by its height (h), i.e. 2πr x h = 2πrh.

*Hence, the surface area of a cylinder formula becomes*

where SAcylinder = surface area of cylinder.

Let's take a look at an example calculation

Consider a cylinder with radius (r) 1cm
and height (h) 5cm (where cm = centimeters) - calculate its surface area.

SAcylinder

= 2πr² + 2πrh

= (2 x π x 1²) + (2 x π x 1 x 5)

= 37.7cm² (square centimeters) to 1 d.p. (one decimal place)

Remember to use the left and right bracket buttons on your calculator.

*The calculator key strokes are left bracket, 2, multiply sign (x), pi sign (**π), multiply sign (x), 1, **squared sign (x**²), right bracket, add sign (**+**), left bracket, 2, multiply sign, **pi sign (**π), multiply sign (x), 1, multiply sign (x), 5, right bracket, *equals sign (=). Your calculator should display 37.69911184 which is 37.7 to 1 d.p. You may need to access *x**² and* *π* via a shift or 2nd function button.

## Another example

Work out SAcylinder given r = 2cm and h = 10cm.

SAcylinder

= 2πr² + 2πrh

= (2 x π x 2²) + (2 x π x 2 x 5)

= 88.0cm² (square centimeters) to 1 d.p. (one decimal place)

*See if you get this answer on your calculator - 88.0**cm² is rounded up from the 87.9645943 which should be displayed on your calculator screen at the end of your calculation.*

## You may also be interested in ...

Volume of a cylinder

Volume of a cone

Surface area of a cone

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Surface area of a cylinder